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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
169.a.169.1 169.a \( 13^{2} \) $0$ $\Z/19\Z$ \(\mathrm{M}_2(\Q)\) $[4,793,3757,-21632]$ $[1,-33,-43,-283,-169]$ $[-1/169,33/169,43/169]$ $y^2 + (x^3 + x + 1)y = x^5 + x^4$
196.a.21952.1 196.a \( 2^{2} \cdot 7^{2} \) $0$ $\Z/6\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[1340,1345,149855,2809856]$ $[335,4620,90160,2214800,21952]$ $[4219140959375/21952,6203236875/784,12905875/28]$ $y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$
324.a.648.1 324.a \( 2^{2} \cdot 3^{4} \) $0$ $\Z/21\Z$ \(\mathrm{M}_2(\Q)\) $[60,945,2295,82944]$ $[15,-30,140,300,648]$ $[9375/8,-625/4,875/18]$ $y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
676.b.17576.1 676.b \( 2^{2} \cdot 13^{2} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[1244,1249,129167,2249728]$ $[311,3978,72332,1667692,17576]$ $[2909390022551/17576,4602275343/676,10349147/26]$ $y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
784.c.614656.1 784.c \( 2^{4} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[398,9016,912086,2401]$ $[796,2358,-2348,-1857293,614656]$ $[1248318403996/2401,9291226221/4802,-23245787/9604]$ $y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$
1296.a.20736.1 1296.a \( 2^{4} \cdot 3^{4} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[78,216,4806,81]$ $[156,438,-428,-64653,20736]$ $[4455516,160381/2,-18083/36]$ $y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$
2187.a.6561.1 2187.a \( 3^{7} \) $0$ $\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[124,297,13275,3456]$ $[93,249,-239,-21057,6561]$ $[28629151/27,2472653/81,-229679/729]$ $y^2 + (x^3 + 1)y = -1$
2704.a.43264.1 2704.a \( 2^{4} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[110,520,15470,169]$ $[220,630,-620,-133325,43264]$ $[2013137500/169,52408125/338,-468875/676]$ $y^2 = x^5 - 5x^3 - 5x^2 - x$
2916.a.5832.1 2916.a \( 2^{2} \cdot 3^{6} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[4,369,1257,-3072]$ $[3,-138,-356,-5028,-5832]$ $[-1/24,23/36,89/162]$ $y^2 + (x^3 + 1)y = x^3$
3721.a.3721.1 3721.a \( 61^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[196,6649,304573,-476288]$ $[49,-177,-187,-10123,-3721]$ $[-282475249/3721,20823873/3721,448987/3721]$ $y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$
3969.b.35721.1 3969.b \( 3^{4} \cdot 7^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[268,2961,216951,18816]$ $[201,573,-563,-110373,35721]$ $[1350125107/147,57445733/441,-2527307/3969]$ $y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$
3969.c.35721.1 3969.c \( 3^{4} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[268,2961,216951,18816]$ $[201,573,-563,-110373,35721]$ $[1350125107/147,57445733/441,-2527307/3969]$ $y^2 + (x^2 + x)y = x^5 - 5x^4 + 4x^3 - x$
5184.a.46656.1 5184.a \( 2^{6} \cdot 3^{4} \) $0$ $\Z/6\Z$ \(\mathrm{M}_2(\mathsf{CM})\) $[76,252,5160,24]$ $[228,654,-644,-143637,46656]$ $[39617584/3,1495262/9,-58121/81]$ $y^2 + x^3y = x^3 + 2$
6075.a.18225.1 6075.a \( 3^{5} \cdot 5^{2} \) $0$ $\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[164,2745,106365,-9600]$ $[123,-399,-409,-52377,-18225]$ $[-115856201/75,9166493/225,687529/2025]$ $y^2 + (x^3 + 1)y = x^3 + 1$
8281.b.405769.1 8281.b \( 7^{2} \cdot 13^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[2596,375193,248614093,51938432]$ $[649,1917,-1907,-1228133,405769]$ $[115139273278249/405769,524030063733/405769,-803230307/405769]$ $y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$
8281.c.405769.1 8281.c \( 7^{2} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[2596,375193,248614093,51938432]$ $[649,1917,-1907,-1228133,405769]$ $[115139273278249/405769,524030063733/405769,-803230307/405769]$ $y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x$
8649.b.700569.1 8649.b \( 3^{2} \cdot 31^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1132,73377,21088959,369024]$ $[849,2517,-2507,-2115933,700569]$ $[1815232161643/2883,19016091893/8649,-200783123/77841]$ $y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1$
8649.c.700569.1 8649.c \( 3^{2} \cdot 31^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1132,73377,21088959,369024]$ $[849,2517,-2507,-2115933,700569]$ $[1815232161643/2883,19016091893/8649,-200783123/77841]$ $y^2 + (x^2 + x)y = x^5 + 9x^4 + 13x^3 + 4x^2 - x$
11881.a.11881.1 11881.a \( 109^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[484,6649,988957,1520768]$ $[121,333,-323,-37493,11881]$ $[25937424601/11881,589929813/11881,-4729043/11881]$ $y^2 + (x^2 + x)y = x^5 - 3x^4 + 2x^2 - x$
12321.a.36963.1 12321.a \( 3^{2} \cdot 37^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[4,6697,85285,-4731264]$ $[1,-279,-1107,-19737,-36963]$ $[-1/36963,31/4107,41/1369]$ $y^2 + (x^3 + x + 1)y = x^5 + 3x^4 + 4x^3 + 2x^2$
12544.a.12544.1 12544.a \( 2^{8} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[62,112,2114,49]$ $[124,342,-332,-39533,12544]$ $[114516604/49,5094261/98,-79763/196]$ $y^2 = x^5 + 2x^4 - x^3 - 3x^2 - x$
12544.c.12544.1 12544.c \( 2^{8} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[62,112,2114,49]$ $[124,342,-332,-39533,12544]$ $[114516604/49,5094261/98,-79763/196]$ $y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x$
12544.i.614656.1 12544.i \( 2^{8} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[398,9016,912086,2401]$ $[796,2358,-2348,-1857293,614656]$ $[1248318403996/2401,9291226221/4802,-23245787/9604]$ $y^2 = x^5 + 4x^4 - 13x^3 + 9x^2 - x$
13689.a.13689.1 13689.a \( 3^{4} \cdot 13^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[516,8073,1250613,1752192]$ $[129,357,-347,-43053,13689]$ $[441025329/169,9461333/169,-641603/1521]$ $y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 - 2x^2$
13689.b.13689.1 13689.b \( 3^{4} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[516,8073,1250613,1752192]$ $[129,357,-347,-43053,13689]$ $[441025329/169,9461333/169,-641603/1521]$ $y^2 + (x^2 + x)y = x^5 + 3x^4 + x^3 - 2x^2 - x$
15552.c.746496.1 15552.c \( 2^{6} \cdot 3^{5} \) $0$ $\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[142,1368,47940,-12]$ $[852,-2586,-2596,-2224797,-746496]$ $[-1804229351/3,154259641/72,3271609/1296]$ $y^2 + x^3y = 3x^3 + 8$
15876.b.222264.1 15876.b \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) $0$ $\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[636,6129,310743,28449792]$ $[159,798,16268,487452,222264]$ $[1254586479/2744,2828663/196,233147/126]$ $y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 4x^4 + 4x^3 - 5x^2 + 2x - 1$
17689.a.17689.1 17689.a \( 7^{2} \cdot 19^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[580,11305,1902565,2264192]$ $[145,405,-395,-55325,17689]$ $[64097340625/17689,1234693125/17689,-8304875/17689]$ $y^2 + (x^2 + x)y = x^5 - 4x^4 + 2x^3 + x^2 - x$
17689.b.17689.1 17689.b \( 7^{2} \cdot 19^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[580,11305,1902565,2264192]$ $[145,405,-395,-55325,17689]$ $[64097340625/17689,1234693125/17689,-8304875/17689]$ $y^2 + (x^3 + x + 1)y = -3x^4 - 3x^3 + x^2 + x$
18225.a.18225.1 18225.a \( 3^{6} \cdot 5^{2} \) $1$ $\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[196,1305,73965,9600]$ $[147,411,-401,-56967,18225]$ $[282475249/75,16117913/225,-962801/2025]$ $y^2 + (x^3 + 1)y = 1$
20736.a.20736.1 20736.a \( 2^{8} \cdot 3^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[78,216,4806,81]$ $[156,438,-428,-64653,20736]$ $[4455516,160381/2,-18083/36]$ $y^2 = x^5 + x^4 - 3x^3 - 4x^2 - x$
20736.f.186624.1 20736.f \( 2^{8} \cdot 3^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[74,288,5502,3]$ $[444,1302,-1292,-567213,186624]$ $[277375828/3,10991701/18,-442187/324]$ $y^2 = x^5 - 2x^4 - 9x^3 - 7x^2 - x$
20736.g.186624.1 20736.g \( 2^{8} \cdot 3^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[74,288,5502,3]$ $[444,1302,-1292,-567213,186624]$ $[277375828/3,10991701/18,-442187/324]$ $y^2 = x^5 + 2x^4 - 9x^3 + 7x^2 - x$
21316.a.42632.1 21316.a \( 2^{2} \cdot 73^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[196,12337,588745,-5456896]$ $[49,-414,-908,-53972,-42632]$ $[-282475249/42632,24353343/21316,545027/10658]$ $y^2 + (x^3 + x + 1)y = 3x^3 + 4x^2 + x$
21904.e.350464.1 21904.e \( 2^{4} \cdot 37^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[302,5032,388574,1369]$ $[604,1782,-1772,-1061453,350464]$ $[314010903004/1369,3067669341/2738,-10100843/5476]$ $y^2 = x^5 + 3x^4 - 11x^3 + 8x^2 - x$
24649.a.24649.1 24649.a \( 157^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[676,17113,3248173,3155072]$ $[169,477,-467,-76613,24649]$ $[137858491849/24649,2302387893/24649,-13337987/24649]$ $y^2 + (x^2 + x)y = x^5 + 4x^4 + 3x^3 - x^2 - x$
26244.c.157464.1 26244.c \( 2^{2} \cdot 3^{8} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[60,945,2295,82944]$ $[45,-270,3780,24300,157464]$ $[9375/8,-625/4,875/18]$ $y^2 + (x^3 + 1)y = 2x^3$
26244.d.314928.1 26244.d \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[24,189,1107,-162]$ $[72,-918,-3024,-265113,-314928]$ $[-6144,1088,448/9]$ $y^2 + y = x^6 - 2x^3$
26244.e.472392.1 26244.e \( 2^{2} \cdot 3^{8} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[356,3969,419553,248832]$ $[267,1482,-2884,-741588,472392]$ $[5584059449/1944,174127343/2916,-5711041/13122]$ $y^2 + (x^3 + 1)y = 2$
32761.a.32761.1 32761.a \( 181^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[676,41449,6681253,-4193408]$ $[169,-537,-547,-95203,-32761]$ $[-137858491849/32761,2591996433/32761,15622867/32761]$ $y^2 + (x^3 + x + 1)y = x^5 + 10x^2 + 19x + 10$
37636.a.602176.1 37636.a \( 2^{2} \cdot 97^{2} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[196,28033,1517953,-77078528]$ $[49,-1068,-4912,-345328,-602176]$ $[-282475249/602176,31412283/150544,737107/37636]$ $y^2 + (x^3 + x + 1)y = x^5 + 4x^4 + 6x^3 + 3x^2$
38416.a.614656.1 38416.a \( 2^{4} \cdot 7^{4} \) $2$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[398,9016,912086,2401]$ $[796,2358,-2348,-1857293,614656]$ $[1248318403996/2401,9291226221/4802,-23245787/9604]$ $y^2 = x^6 - 3x^5 - x^4 + 7x^3 - x^2 - 3x + 1$
43264.c.43264.1 43264.c \( 2^{8} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[110,520,15470,169]$ $[220,630,-620,-133325,43264]$ $[2013137500/169,52408125/338,-468875/676]$ $y^2 = x^5 - 5x^3 + 5x^2 - x$
46656.c.93312.1 46656.c \( 2^{6} \cdot 3^{6} \) $1$ $\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[44,9,357,48]$ $[132,672,-1264,-154608,93312]$ $[1288408/3,149072/9,-19118/81]$ $y^2 + x^3y = x^3 - 1$
48841.b.830297.1 48841.b \( 13^{2} \cdot 17^{2} \) $0$ $\mathsf{trivial}$ \(\mathrm{M}_2(\Q)\) $[764,10777,650195,106278016]$ $[191,1071,30923,1189813,830297]$ $[254194901951/830297,438975873/48841,3903467/2873]$ $y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 5x^4 + 6x^3 - 6x^2 + 2x - 1$
52441.a.52441.1 52441.a \( 229^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[964,41449,10706437,6712448]$ $[241,693,-683,-161213,52441]$ $[812990017201/52441,9700282053/52441,-39669323/52441]$ $y^2 + (x^2 + x)y = x^5 + 5x^4 + 5x^3 - x$
59049.a.177147.1 59049.a \( 3^{10} \) $1$ $\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[52,-63,-111,384]$ $[117,783,-2079,-214083,177147]$ $[371293/3,63713/9,-13013/81]$ $y^2 + (x^3 + 1)y = x^3 - 1$
62208.n.746496.1 62208.n \( 2^{8} \cdot 3^{5} \) $0$ $\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[142,1368,47940,-12]$ $[852,-2586,-2596,-2224797,-746496]$ $[-1804229351/3,154259641/72,3271609/1296]$ $y^2 = x^6 - 3x^3 + 2$
72900.a.291600.1 72900.a \( 2^{2} \cdot 3^{6} \cdot 5^{2} \) $1$ $\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[184,1845,87015,150]$ $[552,1626,-1616,-883977,291600]$ $[13181630464/75,211024448/225,-3419456/2025]$ $y^2 + y = x^6 - 2x^3 + 1$
72900.b.291600.1 72900.b \( 2^{2} \cdot 3^{6} \cdot 5^{2} \) $0$ $\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[184,1845,87015,150]$ $[552,1626,-1616,-883977,291600]$ $[13181630464/75,211024448/225,-3419456/2025]$ $y^2 + x^3y = 2x^3 + 5$
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